A Swirl of disagreements over the terms of Gov. Cuomo’s assault-rifle gun ban, his demand for more restrictions on legal gun ownership, tougher criminal penalties for illegal gun use and requirements that mental-health professionals report the names of potential mass killers has put into doubt a vote on the measure this week.

Cuomo administration and legislative insiders told The Post several major areas of disagreement still exist, with the strongest differences occurring between Senate GOP leaders and negotiators for the Democrat-controlled Assembly.

Negotiators have apparently agreed on a key sweeping change in the state’s gun laws having nothing to do with the assault-rifle controversy, sources said.

The agreement would prohibit an individual from selling any rifle or a shotgun — including even a small, .22-caliber, single-shot rifle — to another person without having first cleared the sale through a federally sponsored NICS (National Instant Criminal Background Check System) conducted by a licensed gun dealer.

One of the state’s best-known gun dealers, calling the requirement “unconstitutional,’’ said such a law “would effect tens of thousands, and possibly hundreds of thousands, of legal gun sales’’ annually.

Cuomo, who pledged in his State of the State last week to pass the toughest gun restrictions in the nation, has, meanwhile, made it clear in private that he isn’t interested in trying to “confiscate’’ the million-plus military-style assault rifles believed to be legally possessed by New Yorkers — despite his controversial suggestion a few weeks ago that such a possibility was on the table.

Despite public claims to the contrary, Assembly Speaker Sheldon Silver (D-Manhattan) was described as resisting stronger criminal penalties sought by Cuomo and Senate Republican Leader Dean Skelos (R-Nassau) for gun-related crimes, a Democrat familiar with the negotiations said.

Skelos was also warning that the anti-gun measure could lead to the closing of the historic Remington Arms Co. factory — maker of the controversial Bushmaster rifle — in the economically hard-pressed village of Ilion in upstate Herkimer County, which provides 1,000 desperately needed jobs.

Silver, meanwhile, was described as holding out for a broader definition of the semiautomatic assault rifles that are to be banned than the one sought by Skelos and possibly even Cuomo, the insiders said.

Also at issue were Democratic proposals to strip counties of their authority to decide how long permits issued to legal handgun owners are good for and to impose a mandatory expiration date — probably five years — instead.

Democrats were also pushing to require all current owners of assault-style rifles to be forced to register them with the state for a period of no longer than five years, with all renewals subject to a NICS background check. The Democrats would also prohibit the sale of the already privately possessed rifles within the state.

By last night, rumors swirled that Cuomo would require the Legislature to remain in session all this week to get a gun measure passed. Some Senate Republicans claimed Cuomo had threatened to use a controversial “message of necessity’’ that waives the normal three-day waiting period before a bill can be voted on in order to deny opponents of the measure time to mobilize.

A Cuomo administration source denied there was any intention to hold the Legislature in Albany if an agreement wasn’t reached or to use a message of necessity, which the governor has said in the past shouldn’t be used to circumvent public comment periods.

Meanwhile, the source said, Cuomo expects many liberal Democrats to oppose the requirement that mental-health professionals, such as psychiatrists and psychologists, report the names of mentally disturbed patients who may be preparing to carry out mass killings like the Newtown, Conn., school massacre, which shocked the nation.

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Mayor Bloomberg has decided to spread his wealth and perhaps hedge his traditional political bets with a first-time-ever significant contribution to Assembly Democrats led by Silver, The Post has learned.

Campaign records set to be filed tomorrow with the state Board of Elections will show that Bloomberg contributed $250,000 to the Assembly Democratic Campaign Committee – the first such contribution he’s made during his 11 years in office.

Bloomberg, a onetime Democrat turned Republican turned independent, has traditionally made major contributions to Senate Republicans — including a highly publicized donation of $1 million last September.

Until now he’s never contributed to Assembly Democrats — partly because of clashes with Silver over the proposed Westside Stadium and the “congestion pricing’’ plan to limit vehicle traffic in most of Manhattan.

“Speaker Silver and the mayor have worked to repair and improve their relationship and over the last several ears they’ve increasingly become friendly,’’ said Deputy Mayor Howard Wolfson, when asked about Bloomberg’s decision to help fund the Democrats.

“The mayor has also found Speaker Silver and the Assembly particularly helpful in working on the five borough taxi plan that we have pursued and he felt that the speaker and the Assembly Democrats merited support,’’ he continued.